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Choquet-Bruhat Y., Dewitt-Morette C. — Analysis, manifolds and physics
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Название: Analysis, manifolds and physicsАвторы: Choquet-Bruhat Y., Dewitt-Morette C. Аннотация: This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled ``Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2Год издания: 1982Количество страниц: 630Добавлена в каталог: 12.01.2014Операции: Положить на полку |
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O-chain 223 O-form 223 Objects 3 Odd forms 212 One parameter group 117 One parameter subgroup 153 One parameter variation 345 One point compactification 16 One-form 138 One-one 3 Onto 3 Open ball 424 Open mapping theorem 63 Open set 12 Operation 6 Operation, external 6 Operation, internal 6 Operators 6 Order (of a) differential equation 492 Order (of a) distribution 437 Order (of a) linear differential operator 485 Order (of a) tensor 139 ordered 6 Ordered, linearly 6 Ordered, totally 6 Ordering 5 Ordering, partial 5 Orientable 212 Orientation 212 Orthonormal basis 31 287 p-chain 217 p-compound matrix 199 270 p-form 195 p-rectangle 216 p-simplex 216 Palais — Smale condition 568 Paley — Wiener theorem 477 Parabolic equation 494 510 Paracompact 16 Parallel along a curve 302 Parallel translation 302 Parallel transport 302 358 369 Partial derivative 74 Partial differential equations 492 Partial ordering 5 Partition 2 Partition of unity 214 Passive viewpoint 406 Past compact 524 Past directed 288 Pauli algebra 64 Pauli matrices 183 Period 227 Pfaff derivative 138 Pfaff system 229 236 242 Pfaff system of vector fields 248 Phase space 169 265 Picard method 96 Plancherel theorem 490 Poincare duality theorem 228 Poincare lemma 225 Poincare — Hopf theorem 396 Point spectrum 60 Poisson bracket 270 Poisson equation 495 Polar coordinates 411 Polynomial invariant 392 Pontrijagin class 394 Pontrijagin number 396 Positive 11 Positive distribution 495 Positive measure 35 Positive set function 34 Positive, strictly 11 Potential 364 496 Potential, general formula 496 Potential, surface 499 Potential, surface dipole 499 Power set 2 Poynting vector 338 Pre-Hilbert 11 Principal fibre bundle 129 Principal part 492 Principal symbol 397 Principal value 439 532 Probability space 36 Product by 424 Product measure 37 Product topology 20 Product, cartesian 2 Product, tensor 140 Projectable vector field 135 Projection mapping 20 Projective space 188 Projective system 575 Projective topology 18 Promeasure 576 Propagators 522 525 Proper manifold 285 Proper riemannian manifold 285 Proper riemannian structure 292 Proper subset 2 Pseudo-metric 556 Pseudo-riemannian 285 Pseudoparticle 414 Pull back 116 203 551 Pure gauge 414 Pure radiation field 339 Quadratic form 80 Quasi-linear equation 518 Quasi-linear systems 520 Quaternion 66 Quotient group 7 Radon measure 48 Raising indices 286 RANGE 2 Rank (of a) mapping 72 Rank (of a) p-form 230 Rank (of a) Pfaff system 242 Rank (of an) ideal 233 Real analytic manifold 112 Real representation of GL(n, C) 332 Realization 162 Reciprocal image 116 138 203 551 Reducible 131 Reduction of a principal fibre bundle 131 381 Reeb theorem 592 refinement 15 Reflexive 59 Regular 8 550 Regular Borel measure 36 Regular embedding 550 Regular measure 438 Regular set function 36 Regularity theorem 495 Regularization 433 Regularization of a distribution 465 Regularizing 432 Relation 5 Relative integral invariant 264 Relative minimum 82 Relative topology 20 Relatively compact 16 Representation 163 Representative 543 544 546 Residual spectrum 60 Response 530 Restricted holonomy group 387 Restriction of a mapping 3 Ricci tensor 309 Riemann connection 308 Riemann curvature scalar 310 Riemann curvature tensor 309 Riemann integral 32 47 Riemann manifold 285 555 Riesz representation theorem 56 Riesz theorem 31 55 Riesz — Fischer theorem 52 Riesz — Markov theorem 48 Riesz — Schauder theorem 63 Right action 129 163 Right differential 179 Right elementary solution 470 Right invariant form 208 Right invariant vector field 155 Right translation 154 Ring 8 Ring of subsets 33 Ring with identity 8 Ring, factor 8 Ring, quotient 8 Rotation 181 Salam — Weinberg model 402 Sard theorem 559 Scalar product 11 285 Scale property 25 Schauder fixed point theorem 565 Schrodinger equation 528 Schwarz inequality 11 Schwarzschild solution 341 Second countable 14 Second fundamental form 312 Second variation 79 Section 132 363 Self-adjoint 59 Semi regular 471 Seminorm 26 423 Semisimple Lie group 188 Separable 13 Separated 13 Separated family (of seminorms) 425 SEQUENCE 3 14 Sequence, Cauchy 23 25 Sequential Wiener integral 587 Sequentially complete 23 Sesquilinear mapping 10 Sesquilinear, non degenerate 11 Sesquilinear, positive 11 Sesquilinear, strictly positive 11 Set 1 Set, Borel 34 Set, bounded 23 Set, closed 13 Set, countable 3 Set, countably infinite 3 Set, directed 5 Set, empty 1 Set, null 1 Set, open 12 Set, power 2 Set, subset 1 Set, void 1 Shock wave 535 Signature 287 Signed measure 49 Simple function 41 Simple Lie group 188 simplex 216 Simply connected 19 Singular field 339 Singular points 386 Small disturbance equation 105 Smooth function 195 SO(3) and SU(2) 181 SO(n), SU(n) 173 Soap bubble problem 105 Soap film problem 277 Sobolev inequalities 491 Sobolev spaces 486 Soldering form 376 Solution of a system of exterior equations 229 Space 487 491 Space 52 Space 53 Space 486 Space 428 Space 29 Space 427 Space 435 Space 474 476 Space (of) paths 593 Space, Banach 28 Space, Euclidean 299 Space, first countable 14 Space, flat 299 Space, Frechet 26 Space, function 574 Space, Hilbert 30 Space, Hoelder 70 Space, linear 9 Space, Minkowski 299 Space, pre-Hilbert 11 Space, second countable 14 Space, topological vector 21 Space, vector 9 Spacelike 288 517 Spacetime 414 Spectrum 60 Spectrum, continuous 60 Spectrum, point 60 Spectrum, residual 60 Sphere 20 190 Spin bundle 417 Spin connection 415 419 Spin frame 415 Spin structure 415 Spin tensor 418 Spin(4) 64 Spinor 415 Spinor field 418 Spray 556 Standard horizontal vector field 378 Star dual 295 Star operator 294 295 State space 265 Stationary 119 322 Stationary phase 593 Steifel — Whitney class 418 Step function 41 42 Step mapping 50 Stereographic 192 410 Stokes' theorem 216 Strain tensor 177 Strict components 197 Strict relative minimum 82 Strictly hyperbolic 516 Strong topology 30 Structural equations 373 376 Structural group 125 Structure coefficients 306 Structure constants 156 Subcovering 15 Subgroup 7 Subharmonic distribution 496 Submanifold 239 547 Submersion 242 550 Subnet 15 Subset 1 Subset, proper 2 Subset, rings of subsets 33
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